Let f ( x ) be a continuous function on [ a, b ] and differentiable on ( a, b ). Then, this function f ( x ) is strictly increasing in ( a, b ) if

Let $\displaystyle \mathrm{f}(\mathrm{x})$ be a continuous function on $\displaystyle [\mathrm{a}, \mathrm{b}]$ and differentiable on $\displaystyle (\mathrm{a}, \mathrm{b})$. Then, this function $\displaystyle \mathrm{f}(\mathrm{x})$ is strictly increasing in $\displaystyle (\mathrm{a}, \mathrm{b})$ if